For the following dataset, enter the data into a calculator and find the least squares regression line, correlation coefficient, and coefficient of determination. remember to show your thinking through your work. . x1: 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5. y1: 8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68

The correct answers are:

y = 0.5x+3; r = 0.816; and r² = 0.667.

Explanation:

Plotting the x-values into List 1 and the y-values into List 2, then running the regression, we get an equation of the form y=ax+b, where a = 0.500 and b = 3.000.  This means the rate of change, or slope, of the regression line is 0.5 (up one and over 2 between points) and the y-intercept is 3 (the data crosses the y-axis at (0, 3)).

The r-value, or correlation coefficient, tells us how closely the regression fits the line.  Since it is 0.816, which is fairly close to 1, this is a good fit.

The r²-value, or coefficient of determination, shows percentage variation in y which is explained by all the x variables together.  The value of r² is always between 0 and 100%;  0% indicates that the model explains none of the variability of the response data around its mean, while 100% indicates that the model explains all the variability of the response data around its mean.  Since the value of r² is 0.667, or 66.7%, this means that it is a fairly good fit.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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